Mo Farah ambles around an empty track at St Mary's University College in Twickenham with his five-year-old daughter, Rihanna, perched on his shoulders and two gold medals swinging gently from his neck. On a stormy summer afternoon his face is lit by a smile so wide it almost erases the memory of the pain that contorted his features on the final straight of the 5,000m at the European Championships 10 days ago. His relaxed mood also conjures up an easy contrast with the scream he unleashed as he crossed the line in Barcelona to complete his 5,000m and 10,000m double.

"That scream just came out," Farah says quietly, once he has left his little girl and his medals with his wife, Tania, and slipped inside the trackside cafe. "After the 10k I didn't go too crazy because I was thinking about the 5,000 final I still had to run. But when I won the 5k it was just …"

Farah shakes his head as the words elude him. "It's so hard to explain. All I can say is that in my head I was thinking, 'Oh my God, I've done it!' And then I turned to see my family and I thought of everything we'd been through. The emotion just got to me."

The depth of Farah's commitment to running is illustrated by his recent honeymoon with Tania. They first met, and started going out together, when they were at the same school in a humdrum stretch of Hounslow, beneath the Heathrow flight path, 12 years ago. Farah was still settling into his strange new life in west London, having arrived from Somalia with only a few words of English when he was nine in 1992. And so this April there was relief and happiness when they finally found the time in Farah's crammed schedule to hold their wedding.

"It was great," Farah says, "and then we went on honeymoon. We had two weeks in Zanzibar. I still ran every other day but it was a proper honeymoon – until we realised we weren't sure how we were going to get home because of the volcanic ash. We were in Nairobi for three days and I could feel myself losing fitness.

"I said to Tania, 'I think I need to go up in the mountains [in Kenya] and you need to go home on your own. It's not too far away now, the Europeans, and I've got to get my fitness back.' She could've said, 'I'm not flying home on my own from my honeymoon.' But, straightaway, she said, 'You've got to think of yourself on that start line and get the best preparation.' She's very unselfish so she flew home, alone, and I went up into the mountains.

"We've not spent a lot of time together since we got married and that's why winning both the 5 and the 10k felt so sweet. It made the sacrifice worth it. And it wasn't no overnight success. It's taken us years to get to this point where eating, sleeping, training and racing all came just right."

Farah's pride sounds apt when set against the disappointments that have studded his career. Four years ago, in the European 5,000m final, he lost the lead on the final straight as Jesús España swept past him. That hurtful defeat prompted Farah's decision to start training with a group of leading Kenyan runners who, sharing his agent, Ricky Simms, had based themselves in Teddington. But even his immersion in a stark African running culture could not prevent his poor performance at the Beijing Olympics when he failed to qualify for the 5,000m final.

The real transformation began 18 months ago as, after Beijing, Farah switched to rigorous training camps with his Kenyan crew at Kaptagat – in the mountains above the Great Rift Valley. After his first two-month session of Kenyan seclusion he won the European Indoor 3,000m in March 2009. That victory, however, was followed by more frustration as he finished seventh in the 5,000m at the World Championships last August.

"I was a second-and-a-half off a medal," he says, "but I was so disappointed. The difference between seventh and winning a medal is massive."

But in his third ever 10,000m race, in the European final, Farah was in such control he jokingly cajoled other runners to take the lead. Farah was especially exuberant towards his friend and team-mate, Chris Thompson. "I was so confident," he says, "I turned to Chris and waved him on. I wanted to say, 'C'mon, mate, we're not going fast. You can win a medal here.' And of course Chris got the silver. I was so happy but I didn't sleep much that night. I couldn't stop thinking about the 5K."

Did Farah have to conquer any doubts after his failure against España in 2006? "In training I thought about him a lot. I also studied that race when he beat me. It might look simple but, mentally, you need to get over that hurdle. So that's why, up here [Farah taps his head], I'm really stronger. I've been through so many ups and downs. But, on that last straight, I gritted my teeth and pushed hard. I didn't know how far ahead I was of España, and I was really hurting, but I wouldn't allow him to beat me."

Farah's twin victories symbolised the resurgence of the British team in Barcelona as they achieved their best result in a European Championships by winning 19 medals. Yet it is sobering to remember that Farah is ranked the 24th best performer over 5,000m this year. His personal best of 13min 05.66sec, set in Gateshead at the start of the summer, is five seconds short of the British record. Dave Moorcroft's supreme run of 13:00.41 in 1982 eludes Farah while the current world record remains in another dimension. Six years ago, Kenenisa Bekele, the extraordinary Ethiopian, ran a race that still shocks Farah.

"Bekele's time [12:37.35] is unbelievable. I've watched that race and it's incredible – it's the same feeling I get when I watch his race in Brussels where he broke the 10K world record [in 2005]. He's a great, great athlete. But in the 5,000m he has slowed a bit every year since then [with that gradual decline continuing as his best time last season was 12.52.32]. He's had injuries and he got married, and then he lost his wife, and he married again."

Yet surely the discrepancy between him and Bekele undermines claims that Farah could win an Olympic medal in 2012? "I think it's a realistic target," he says. "It's fine to run fast times but it's important to mix it up with medals. You have to believe in yourself and at the World Championships last year I was two-and-a-half seconds away from Bekele [who ran 13:17.09]. He's beatable. Joseph Ebuya, who I train with in Kenya, beat Bekele in cross-country this year. Joseph was holding his head, saying, 'I beat him, I beat him …' So Bekele can have an off‑day.

"In 2012 I think 12:50 would definitely win it – and it could even be 13:10 or 13:15. If you look at every major championship a time around 13 minutes usually wins it. So I can definitely win a medal at the worlds next year and at the London Olympics. On my day I know it's possible."

First, as much psychologically as practically, he needs to break Moorcroft's British record – set nine months before the 27-year-old Farah was born. "I have to do it," he says. "I must break that record. I've got to knock off five seconds over 12 laps. Less than half a second a lap? Mmmmm. Sounds easy, don't it? But it's a barrier I have to get past. I have to go under 13 minutes to prove I can win medals at the worlds and Olympics. That's the next level and I'm nearly there.

"I'm going to run at Crystal Palace next week in a 3,000m, which will be good, as I ran well there last year. I'll also be in front of my home crowd. But the Europeans took a lot out of me so I'm going to see how I run. If that goes well I'll target the British 5,000m record before the year is out."

Farah will soon leave his family again to return to Kenya – and that dedication is likely to ensure he surpasses Moorcroft's record. "There's nothing to do in the mountains but run, eat and sleep. The only diversion we've got is this small TV where we can pick up satellite from South Africa and so we get all the football. I see a lot of Arsenal."

As an avid Arsenal fan, Farah cherishes the phone message Arsène Wenger left for him last month. "He said, 'It's Arsène Wenger, well done on your win in the 10,000. It was a great run and I hope you can do the double with the 5,000. Yours sincerely, Arsène Wenger.' I was saying 'No way, no way.'"

There is speculation that Farah might be invited on to the pitch before one of Arsenal's home games this month. "It would be awesome," Farah says. "I would love to do it."

Farah can briefly relish all the attention – with congratulations from Wenger presumably meaning more than appearances on the GMTV sofa with his wife. "I'm actually enjoying it all," he says. "I was on my first run last week and went past these kids playing on a cricket pitch. They started shouting, 'Mo, Mo! Are you Mo?' I shouted 'Hello' and gave them a wave. I'll soon be back to work but it's been great having people give me this acknowledgement. It shows that anything is possible if you keep grafting. That's what I've been doing for years and, at last, it's really paying off."

Tickets for the Aviva London Grand Prix at Crystal Palace on 13-14 August are available on 08000 556 056 or uka.org.uk